WAVES AND STRONGLY SHEARED CURRENTS: EXTENSIONS TO COASTAL OCEAN MODELS
AbstractSignificant progress has been made in the numerical modeling of wave-current interaction during the past decade. Typical coastal circulation and wave models, however, still only employ theoretical formulations which take depth-uniform mean flows into account, with realistic, non-uniform flows treated as being depth uniform through some chosen averaging procedure. Depending on the choice of average over depth, significant errors may arise in the estimation of properties such as group velocity and action density in realistic conditions. These errors, in turn, are fed back into the circulation model through incorrect representation of the vertical structure of wave forcing. A new framework for wave-current interaction theory for strongly sheared mean flows has been developed using vortex force formalism by Dong (2016). The resulting formulation leads to a conservation law for wave action identical to that of Voronovich (1976), and to expressions for wave-averaged forces in the Craik-Leibovich vortex force formalism. In this study, we are completing the development of a coupled NHWAVE/SWAN which implements the wave forcing formulation of Dong (2016) in a wave-averaged version of the non-hydrostatic model NHWAVE (Ma et al., 2012). The SWAN model is also being extended to incorporate a better representation of frequency and direction-dependent group velocity and intrinsic frequency in the neighborhood of the spectral peak, thus improving on the present practice of using quantities evaluated only at the spectral peak. The resulting model is being tested against field data collected in several recent experiments involving strong, vertically sheared currents in river mouths or straits.
Banihashemi, Kirby, Dong (2017). Approximation of the wave action flux velocity in strongly sheared mean flows, Ocean Modeling, 116, 33-47.
Dong (2016): Wave-current interaction in strongly sheared mean flows. University of Delaware PhD thesis.
Kirby, Chen (1989): Surface waves on vertically sheared flows: Approximate dispersion relations, Journal of Geophysical Research, 94, 1013-1027.
Ma, Shi, Kirby (2012): Shock-capturing non-hydrostatic model for fully dispersive surface wave processes, Ocean Modelling, 43-44, 22-35.
McWilliams, Restrepo, Lane (2004): An asymptotic theory for the interaction of waves and currents in coastal waters, Journal of Fluid Mechanics, 511, 135-178.
Thomson, Horner-Devine, Zippel, Rusch, Geyer (2014): Wave breaking turbulence at the offshore front of the Columbia River Plume. Geophysical Research Letters. 41, 8987-8993.
Voronovich (1976): Propagation of internal and surface gravity waves in the approximation of geometrical optics. lzv. Atmos. Oceanic. Phys, 12, 850-857.
Zippel, Thomson (2017): Surface wave breaking over sheared currents: Observations from the Mouth of the Columbia River. J. Geophys. Res: Oceans, 122, 3311- 3328.